secrec The piece you need to recognize is that you don't need to handle a billion connections. G* does only because they route EVERYONE's messages through their servers.
If you run an email server that has a thousand clients, you need to handle around a thousand connections, this is a much more feasible implementation. You also don't need a "unifiedpush". There's no reason for it.
What if you are Signal, with 70 million active users (source)? What if you are a user and you want to get notifications from Signal and WhatsApp on the same phone, and to save battery life you would benefit from the push service delaying one notification a few seconds so it can arrive with another one, and the device wakes up once instead of twice?
secrec Despite some people's claims, there is really no power consumption impact by holding a bunch of open connection to each of the services that you want to receive notifications from.
And yet, users routinely report increased power consumption.
secrec An open connection is really nothing besides states that are held in the routers between your device and the server you are maintaining a connection with.
That's actually not how the Internet works. If your first-hop router uses NAT, there will be NAT state. But the Internet was (carefully!!!) designed so that end-to-end connections do not cost state in every router.